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Simplifying -16x2 + 112x + 160 = 0 Reorder the terms: 160 + 112x + -16x2 = 0 Solving 160 + 112x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 7x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(10 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 10 + 7x + -1x2 = 0 Solving 10 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -7x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -7x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -7x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -7x + x2 = 0 + 10 -7x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -7x + x2 = 10 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 10 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 10 + 12.25 Combine like terms: 10 + 12.25 = 22.25 12.25 + -7x + x2 = 22.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -3.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -3.5 = 4.716990566 Simplifying x + -3.5 = 4.716990566 Reorder the terms: -3.5 + x = 4.716990566 Solving -3.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.716990566 + 3.5 x = 4.716990566 + 3.5 Combine like terms: 4.716990566 + 3.5 = 8.216990566 x = 8.216990566 Simplifying x = 8.216990566Subproblem 2
x + -3.5 = -4.716990566 Simplifying x + -3.5 = -4.716990566 Reorder the terms: -3.5 + x = -4.716990566 Solving -3.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.716990566 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.716990566 + 3.5 x = -4.716990566 + 3.5 Combine like terms: -4.716990566 + 3.5 = -1.216990566 x = -1.216990566 Simplifying x = -1.216990566Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.216990566, -1.216990566}Solution
x = {8.216990566, -1.216990566}
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